Let \(G\) , \(G^{\prime }\)  be Carnot groups, where \(G\)  has dimension \(n\)  and homogeneous dimension \(\nu \) , let \(M\subset G\) , \(M^{\prime }\subset G^{\prime }\)  be open subsets, and \(f:M\rightarrow M^{\prime }\)  be a \(W^{1,p}_{\operatorname{loc}}\) -mapping for some \(p>\nu \) . Then \(f\)  is Pansu differentiable almost everywhere [1]}, [2]} (see also [3]}, [4]}). The Pansu differential \(D_Pf(x):\fg \rightarrow \fg ^{\prime }\)  is a graded homomorphism of Lie algebras, and therefore the pullback \(D_Pf(x)^*:\Lambda ^*\fg ^{\prime *}\rightarrow \Lambda ^*\fg ^*\) 
respects the weight decompositions, i.e.
\(D_Pf(x)^*\Lambda ^{*,p}\fg ^{\prime *}\subset \Lambda ^{*,p}\fg ^*\,.\) 
